Twistorial constructions of spacelike surfaces in Lorentzian 4-manifolds

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We investigate the twistor space and the Grassmannian fibre bundle of a Lorentzian 4-space with natural almost optical structures and its induced CR-structures. The twistor spaces of the Lorentzian space forms $\R^4_1, \Di{S}^4_1$ and $\Di{H}^4_1$ are explicitly discussed. The given twistor construction is applied to surface theory in Lorentzian 4-spaces. Immersed spacelike surfaces in a Lorentzian 4-space with special geometric properties like semi-umbilic surfaces and surfaces that have mean curvature of vanishing lengths correspond to holomorphic curves in the Lorentzian twistor space. For the Lorentzian space forms $\R^4_1, \Di{S}^4_1$ and $\Di{H}^4_1$ those surfaces are explicitly constructed and classified.
Latex2.09, 26 pages

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Differential Geometry, 53A10, 53C50

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http://salesiana.dossiersoluciones.com/handle/123456789/78117

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/9902101
 http://arxiv.org/abs/math/9902101

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arXiv